The United States will "continue to go after ISIL aggressively until it's removed from Syria and from Iraq and finally destroyed," Obama said, using another name for ISIS.
"The world has to be united against terrorism," Obama said, adding that "that's a top priority of ours." He added that "we can and we will" defeat terrorism.
At the same time, he said, ISIS "is not an existential threat" to the U.S.
He was speaking at a news conference in Argentina the day after more than 30 people were killed in terrorist attacks in Brussels.
Without naming GOP presidential candidate Ted Cruz, Obama also slammed the Texas senator's plan to carpet bomb ISIS
when asked about the idea at the news conference.
"Not only is that contrary to our values," the President said, but, he added, "that would be an extraordinary mechanism for ISIL to recruit more people."
The President is in Buenos Aires for the second stop of a Latin America trip that started in Cuba.
It's the first visit by a U.S. president for bilateral talks in almost 20 years and is meant to cement ties with Argentina's newly established centrist government, but Obama mentioned Tuesday's terrorist attacks in Europe in his opening remarks.
Obama was also questioned about political criticism from Republican presidential candidates that his approach to fighting ISIS isn't working and that he's not focused enough on it.
Obama dismissed the suggestion and the approach many in the GOP are advocating.
"When it comes to defending the United States or its allies and our core interests, I will not hesitate to use military force where necessary," Obama said.
"But how we do that is important," he added. "We just don't go ahead and blow something up just so we can go back home and say we blew something up. That's not a foreign policy."
The President pointed to Cruz's own family history as a reason why the latter's policies wouldn't work, particularly his suggestion Tuesday that police patrol American Muslim communities.
"I just left a country that engages in that kind of surveillance," Obama said of his previous stop in Cuba, "which by the way the father of Sen. Cruz escaped for America, the land of the free."
Later Wednesday, Obama described the Republican Party as deeply split after drifting from the "mainstream" in an effort to oppose his policies. But he said the potential damage inflicted by a Republican president wouldn't necessarily be longstanding.
"Even if we end up with someone I might not consider a great president, there's a limit to some of the damage they can do," Obama said, citing the separation of powers in the federal system. "I'm sure Republicans feel the same way about me."
Obama has said previously that he's confident a Democrat will be elected to replace him, and praised both Vermont Sen. Bernie Sanders and his former secretary of state, Hillary Clinton, for addressing income inequality in their campaigns.
But he said that even if neither of them win the White House, the country would be safeguarded from long-term deterioration.
"I'm confident the American people will make a good choice," he said, adding: "We usually can recover from mistakes."
In the earlier news conference, Obama argued that one reason the U.S. has been insulated from more attacks is that its Muslim community is "successful, patriotic, integrated" and not ghettoized.
"Any approach that would single them out and treat them for discrimination would not only be wrong," Obama said, "it would be counterproductive because it would reduce the anti-bodies we have to reduce terrorism."
But he defended the measures he's put in place, saying that airstrikes on ISIS' leaders, infrastructure and financial system, have reduced the terrorist group's territory by about 40%.
He also cited the work of U.S. Special Operations forces working with Iraqis, efforts to go after ISIS couriers and to disrupt the connection between strongholds in Mosul, Iraq, and Raqaa, Syria.
"While we're doing that, we're also extra vigilant" to work to prevent attacks," Obama said, "but as I said before, this is difficult work."
"It's challenging to find, identify very small groups of people who are willing to die themselves and can walk into a crowd and detonate a bomb," Obama said.
The death toll from the attacks at Brussels' airport and the city's Maelbeek metro station now stands at 31, with about 270 people injured and many still unaccounted for, including American citizens.
State Department officials said they are making "every effort" to account for the welfare of all U.S. citizens in the city and are still working through an accounting of all its personnel at the embassy. "Approximately a dozen" Americans were injured in the attack, the officials said.
The suicide attacks, claimed by ISIS, were carried out by a group that included two brothers with a history of violent crimes, Khalid and Ibrahim El Bakraoui, Belgian authorities said.
Belgian media reported that one person was arrested Wednesday, while counterterror official Paul Van Tigchelt warned Wednesday that there were others involved in the plot who remained at large in Belgium and still posed a threat.